Cable Sizing Calculation - Open Electrical.pdf

5/12/13

Cable Sizing Calculation - Open Electrical

Cable Sizing Calculation From Open Electrical

Contents 1 Introduction 1.1 Why do the calculation? 1.2 When to do the calculation? 2 General Methodology 2.1 Step 1: Data Gathering 2.1.1 Load Details 2.1.2 Cable Construction 2.1.3 Installation Conditions 2.2 Step 2: Cable Selection Based on Current Rating 2.2.1 Base Current Ratings 2.2.2 Installed Current Ratings 2.2.3 Cable Selection and Coordination with Protective Devices 2.2.3.1 Feeders 2.2.3.2 Motors 2.3 Step 3: Voltage Drop 2.3.1 Cable Impedances 2.3.2 Calculating Voltage Drop 2.3.3 Maximum Permissible Voltage Drop 2.3.4 Calculating Maximum Cable Length due to Voltage Drop 2.4 Step 4: Short Circuit Temperature Rise 2.4.1 Minimum Cable Size Due to Short Circuit Temperature Rise 2.4.2 Initial and Final Conductor Temperatures 2.4.3 Short Circuit Energy 2.5 Step 5: Earth Fault Loop Impedance 2.5.1 The Earth Fault Loop 2.5.2 Maximum Cable Length 3 Worked Example 3.1 Step 1: Data Gathering 3.2 Step 2: Cable Selection Based on Current Rating 3.3 Step 3: Voltage Drop 3.4 Step 4: Short Circuit Temperature Rise 3.5 Step 5: Earth Fault Loop Impedance 4 Waterfall Charts 5 International Standards file:///C:/Documents and Settings/User/Desktop/Cable Sizing Calculation - Open Electrical.htm

1/14

5/12/13

Cable Sizing Calculation - Open Electrical

5.1 IEC 5.2 NEC 5.3 BS 5.4 AS/NZS 6 Computer Software 7 What next?

Introduction This article examines the sizing of electrical cables (i.e. cross-sectional area) and its implementation in various international standards. Cable sizing methods do differ across international standards (e.g. IEC, NEC, BS, etc) and some standards emphasise certain things over others. However the general principles underlying any cable sizing calculation do not change. In this article, a general methodology for sizing cables is first presented and then the specific international standards are introduced.

Why do the calculation? The proper sizing of an electrical (load bearing) cable is important to ensure that the cable can: Operate continuously under full load without being damaged Withstand the worst short circuits currents flowing through the cable Provide the load with a suitable voltage (and avoid excessive voltage drops) (optional) Ensure operation of protective devices during an earth fault

When to do the calculation? This calculation can be done individually for each power cable that needs to be sized, or alternatively, it can be used to produce cable sizing waterfall charts for groups of cables with similar characteristics (e.g. cables installed on ladder feeding induction motors).

General Methodology All cable sizing methods more or less follow the same basic six step process: 1) Gathering data about the cable, its installation conditions, the load that it will carry, etc 2) Determine the minimum cable size based on continuous current carrying capacity 3) Determine the minimum cable size based on voltage drop considerations 4) Determine the minimum cable size based on short circuit temperature rise 5) Determine the minimum cable size based on earth fault loop impedance 6) Select the cable based on the highest of the sizes calculated in step 2, 3, 4 and 5

Step 1: Data Gathering file:///C:/Documents and Settings/User/Desktop/Cable Sizing Calculation - Open Electrical.htm

2/14

5/12/13

Cable Sizing Calculation - Open Electrical

The first step is to collate the relevant information that is required to perform the sizing calculation. Typically, you will need to obtain the following data: Load Details The characteristics of the load that the cable will supply, which includes: Load type: motor or feeder Three phase, single phase or DC System / source voltage Full load current (A) - or calculate this if the load is defined in terms of power (kW) Full load power factor (pu) Locked rotor or load starting current (A) Starting power factor (pu) Distance / length of cable run from source to load - this length should be as close as possible to the actual route of the cable and include enough contingency for vertical drops / rises and termination of the cable tails Cable Construction The basic characteristics of the cable's physical construction, which includes: Conductor material - normally copper or aluminium Conductor shape - e.g. circular or shaped Conductor type - e.g. stranded or solid Conductor surface coating - e.g. plain (no coating), tinned, silver or nickel Insulation type - e.g. PVC, XLPE, EPR Number of cores - single core or multicore (e.g. 2C, 3C or 4C) Installation Conditions How the cable will be installed, which includes: Above ground or underground Installation / arrangement - e.g. for underground cables, is it directly buried or buried in conduit? for above ground cables, is it installed on cable tray / ladder, against a wall, in air, etc. Ambient or soil temperature of the installation site Cable bunching, i.e. the number of cables that are bunched together Cable spacing, i.e. whether cables are installed touching or spaced Soil thermal resistivity (for underground cables) Depth of laying (for underground cables) For single core three-phase cables, are the cables installed in trefoil or laid flat?

Step 2: Cable Selection Based on Current Rating Current flowing through a cable generates heat through the resistive losses in the conductors, dielectric losses file:///C:/Documents and Settings/User/Desktop/Cable Sizing Calculation - Open Electrical.htm

3/14

5/12/13

Cable Sizing Calculation - Open Electrical

through the insulation and resistive losses from current flowing through any cable screens / shields and armouring. The component parts that make up the cable (e.g. conductors, insulation, bedding, sheath, armour, etc) must be capable of withstanding the temperature rise and heat emanating from the cable. The current carrying capacity of a cable is the maximum current that can flow continuously through a cable without damaging the cable's insulation and other components (e.g. bedding, sheath, etc). It is sometimes also referred to as the continuous current rating or ampacity of a cable. Cables with larger conductor cross-sectional areas (i.e. more copper or aluminium) have lower resistive losses and are able to dissipate the heat better than smaller cables. Therefore a 16 mm2 cable will have a higher current carrying capacity than a 4 mm2 cable. Base Current Ratings International standards and manufacturers of cables will quote base current ratings of different types of cables in tables such as the one shown on the right. Each of these tables pertain to a specific type of cable construction (e.g. copper conductor, PVC insulated, 0.6/1kV voltage grade, etc) and a base set of installation conditions (e.g. ambient temperature, installation method, etc). It is important to note that the current ratings are only valid for the quoted types of cables and base installation conditions. In the absence of any guidance, the following reference based current ratings may be used. Installed Current Ratings When the proposed installation conditions differ from the base conditions, derating (or correction) factors can be applied to the base current ratings to obtain the actual installed current ratings.

Example of base current rating table (Excerpt from IEC 60364-5-52)

International standards and cable manufacturers will provide derating factors for a range of installation conditions, for example ambient / soil temperature, grouping or bunching of cables, soil thermal resistivity, etc. The installed current rating is calculated by multiplying the base current rating with each of the derating factors, i.e.

where

is the installed current rating (A) is the base current rating (A) are the product of all the derating factors

For example, suppose a cable had an ambient temperature derating factor of k amb = 0.94 and a grouping derating file:///C:/Documents and Settings/User/Desktop/Cable Sizing Calculation - Open Electrical.htm

4/14

5/12/13

Cable Sizing Calculation - Open Electrical

factor of k g = 0.85, then the overall derating factor k d = 0.94x0.85 = 0.799. For a cable with a base current rating of 42A, the installed current rating would be Ic = 0.799x42 = 33.6A. In the absence of any guidance, the following reference derating factors may be used. Cable Selection and Coordination with Protective Devices Feeders

When sizing cables for non-motor loads, the upstream protective device (fuse or circuit breaker) is typically selected to also protect the cable against damage from thermal overload. The protective device must therefore be selected to exceed the full load current, but not exceed the cable's installed current rating, i.e. this inequality must be met:

Where

is the full load current (A) is the protective device rating (A) is the installed cable current rating (A)

Motors

Motors are normally protected by a separate thermal overload (TOL) relay and therefore the upstream protective device (e.g. fuse or circuit breaker) is not required to protect the cable against overloads. As a result, cables need only to be sized to cater for the full load current of the motor, i.e.

Where

is the full load current (A) is the installed cable current rating (A)

Of course, if there is no separate thermal overload protection on the motor, then the protective device needs to be taken into account as per the case for feeders above.

Step 3: Voltage Drop A cable's conductor can be seen as an impedance and therefore whenever current flows through a cable, there will be a voltage drop across it, which can be derived by Ohm’s Law (i.e. V = IZ). The voltage drop will depend on two things: Current flow through the cable – the higher the current flow, the higher the voltage drop Impedance of the conductor – the larger the impedance, the higher the voltage drop Cable Impedances file:///C:/Documents and Settings/User/Desktop/Cable Sizing Calculation - Open Electrical.htm

5/14

5/12/13

Cable Sizing Calculation - Open Electrical

The impedance of the cable is a function of the cable size (cross-sectional area) and the length of the cable. Most cable manufacturers will quote a cable’s resistance and reactance in Ω/km. The following typical cable impedances for low voltage AC and DC single core and multicore cables can be used in the absence of any other data. Calculating Voltage Drop For AC systems, the method of calculating voltage drops based on load power factor is commonly used. Full load currents are normally used, but if the load has high startup currents (e.g. motors), then voltage drops based on starting current (and power factor if applicable) should also be calculated. For a three phase system:

Where

is the three phase voltage drop (V) is the nominal full load or starting current as applicable (A) is the ac resistance of the cable (Ω/km) is the ac reactance of the cable (Ω/km) is the load power factor (pu) is the length of the cable (m)

For a single phase system:

Where

is the single phase voltage drop (V) is the nominal full load or starting current as applicable (A) is the ac resistance of the cable (Ω/km) is the ac reactance of the cable (Ω/km) is the load power factor (pu) is the length of the cable (m)

For a DC system:

Where

is the dc voltage drop (V) is the nominal full load or starting current as applicable (A) is the dc resistance of the cable (Ω/km) is the length of the cable (m)

file:///C:/Documents and Settings/User/Desktop/Cable Sizing Calculation - Open Electrical.htm

6/14

5/12/13

Cable Sizing Calculation - Open Electrical

Maximum Permissible Voltage Drop It is customary for standards (or clients) to specify maximum permissible voltage drops, which is the highest voltage drop that is allowed across a cable. Should your cable exceed this voltage drop, then a larger cable size should be selected. Maximum voltage drops across a cable are specified because load consumers (e.g. appliances) will have an input voltage tolerance range. This means that if the voltage at the appliance is lower than its rated minimum voltage, then the appliance may not operate correctly. In general, most electrical equipment will operate normally at a voltage as low as 80% nominal voltage. For example, if the nominal voltage is 230VAC, then most appliances will run at >184VAC. Cables are typically sized for a more conservative maximum voltage drop, in the range of 5 – 10% at full load. Calculating Maximum Cable Length due to Voltage Drop It may be more convenient to calculate the maximum length of a cable for a particular conductor size given a maximum permissible voltage drop (e.g. 5% of nominal voltage at full load) rather than the voltage drop itself. For example, by doing this it is possible to construct tables showing the maximum lengths corresponding to different cable sizes in order to speed up the selection of similar type cables. The maximum cable length that will achieve this can be calculated by re-arranging the voltage drop equations and substituting the maximum permissible voltage drop (e.g. 5% of 415V nominal voltage = 20.75V). For a three phase system:

Where

is the maximum length of the cable (m) is the maximum permissible three phase voltage drop (V) is the nominal full load or starting current as applicable (A) is the ac resistance of the cable (Ω/km) is the ac reactance of the cable (Ω/km) is the load power factor (pu)

For a single phase system:

Where

is the maximum length of the cable (m) is the maximum permissible single phase voltage drop (V) is the nominal full load or starting current as applicable (A) is the ac resistance of the cable (Ω/km)

file:///C:/Documents and Settings/User/Desktop/Cable Sizing Calculation - Open Electrical.htm

7/14

5/12/13

Cable Sizing Calculation - Open Electrical

is the ac reactance of the cable (Ω/km) is the load power factor (pu) For a DC system:

Where

is the maximum length of the cable (m) is the maximum permissible dc voltage drop (V) is the nominal full load or starting current as applicable (A) is the dc resistance of the cable (Ω/km) is the length of the cable (m)

Step 4: Short Circuit Temperature Rise During a short circuit, a high amount of current can flow through a cable for a short time. This surge in current flow causes a temperature rise within the cable. High temperatures can trigger unwanted reactions in the cable insulation, sheath materials and other components, which can prematurely degrade the condition of the cable. As the crosssectional area of the cable increases, it can dissipate higher fault currents for a given temperature rise. Therefore, cables should be sized to withstand the largest short circuit that it is expected to see. Minimum Cable Size Due to Short Circuit Temperature Rise The minimum cable size due to short circuit temperature rise is typically calculated with an equation of the form:

Where

is the minimum cross-sectional area of the cable (mm2) is the prospective short circuit current (A) is the duration of the short circuit (s) is a short circuit temperature rise constant

The temperature rise constant is calculated based on the material properties of the conductor and the initial and final conductor temperatures (see the derivation here). Different international standards have different treatments of the temperature rise constant, but by way of example, IEC 60364-5-54 calculates it as follows: (for copper conductors)

file:///C:/Documents and Settings/User/Desktop/Cable Sizing Calculation - Open Electrical.htm

8/14

5/12/13

Cable Sizing Calculation - Open Electrical

(for aluminium conductors)

Where

is the initial conductor temperature (deg C) is the final conductor temperature (deg C)

Initial and Final Conductor Temperatures The initial conductor temperature is typically chosen to be the maximum operating temperature of the cable. The final conductor temperature is typically chosen to be the limiting temperature of the insulation. In general, the cable's insulation will determine the maximum operating temperature and limiting temperatures. As a rough guide, the following temperatures are common for the different insulation materials:

Material

Max Operating Temperature oC

Limiting Temperature oC

PVC

75

160

EPR

90

250

XLPE

90

250

Short Circuit Energy The short circuit energy is normally chosen as the maximum short circuit that the cable could potentially experience. However for circuits with current limiting devices (such as HRC fuses), then the short circuit energy chosen should be the maximum prospective let-through energy of the protective device, which can be found from manufacturer data.

Step 5: Earth Fault Loop Impedance Sometimes it is desirable (or necessary) to consider the earth fault loop impedance of a circuit in the sizing of a cable. Suppose a bolted earth fault occurs between an active conductor and earth. During such an earth fault, it is desirable that the upstream protective device acts to interrupt the fault within a maximum disconnection time so as to protect against any inadvertent contact to exposed live parts. Ideally the circuit will have earth fault protection, in which case the protection will be fast acting and well within the maximum disconnection time. The maximum disconnection time is chosen so that a dangerous touch voltage does not persist for long enough to cause injury or death. For most circuits, a maximum disconnection time of 5s is sufficient, though for portable equipment and socket outlets, a faster disconnection time is desirable (i.e.